Celebrating Sharadchandra Shrikhande, the Mathematician Who Disproved Euler

Nithyanand Rao in The Wire:

Relatives, well-wishers and dignitaries kept arriving to greet Professor Sharadchandra Shankar Shrikhande. Seated on the lawns, he would adjust his hearing aid –trying to hear over the firecrackers in the background – thank them and smile, and now and then burst into a hearty chuckle, trying not to look in the direction of the intense light drenching the table.

Shrikhande, celebrating his 100th birthday on October 19, 2017, wasn’t too keen to remain in the spotlight. The bright light on the pole was turned away, but visitors kept coming to greet him and seek his blessings, some aware of his great mathematical achievements – in particular, the one that ensured his name would be associated with Leonhard Euler, one of the greatest mathematicians in history. It was 58 years ago that Shrikhande, along with his mentor R.C. Bose and their collaborator E.T. Parker, proved Euler wrong and made the headlines.

Late in his life, the legendary Swiss mathematician Euler (1707–1783) began a long paper pondering a puzzle he couldn’t find an answer to. Although he was almost completely blind by then, his already-prodigious productivity had increased, distractions having been reduced. He had always made the most of his phenomenal memory and ability to calculate in his head and, after his loss of vision, he used a scribe to record his discoveries. The puzzle he was considering was this: Imagine that there are $36$ officers belonging to six different military regiments, each regiment having six officers of different ranks. How does one arrange them in the form of a square such that each row and column has six officers, and no rank or regiment appears more than once in a row and column?

More here.